Adaptive Kalman Filter Research Articles

Error governor for active fault tolerance in PID control of MIMO systems

Input saturation and actuator faults are common issues in control system engineering. This paper proposes an Error Governor (EG) policy that dynamically manages the feedback error to enhance the tracking error in Multiple Input-Multiple Output (MIMO) closed-loop system controlled by Proportional-Integral-Derivative (PID) regulators. By integrating an Adaptive Kalman Filter (AKF) for optimal fault estimation with the EG scheme, the solution enables fault-tolerant control without requiring modifications to the baseline controller, which can be impractical or unsuitable in certain applications. Furthermore, the proposed control scheme completely avoids windup, thereby replacing conventional Anti-Windup (AW) schemes for PIDs, and is computationally cheap and easy to implement, needing only the same inputs as conventional AW algorithms and the actuator fault estimation. Simulation results on the MIMO model of the Zagi flying-wing aerial vehicle show that the EG reduces the tracking error in presence of actuator faults by − 49.92 % in terms of Integral Absolute Error (IAE), outperforming conventional AW methods.

A Nonlinear Suspension Road Roughness Recognition Method Based on NARX-PASCKF.

Road roughness significantly impacts vehicle safety and dynamic responses. For nonlinear suspension systems, the nonlinear characteristics often make it challenging for estimators to identify the actual road roughness accurately. This paper proposes a hybrid road roughness identification algorithm based on nonlinear auto-regressive with exogenous inputs (NARX) and a process noise adaptive square root cubature Kalman filter (PASCKF) to address this issue. Driven by vehicle acceleration data, an NARX-based road roughness identification system is constructed to mitigate the model uncertainties. Furthermore, a hybrid strategy is proposed. On the one hand, the accurate road roughness estimated by the NARX is converted into process noise covariance, enhancing the estimator's accuracy and convergence rate. Another switching strategy is proposed to optimize the non-convergence issues of the PASCKF. Finally, simulation and actual vehicle experiment data demonstrate that this approach offers superior identification accuracy and adaptability compared to the standalone SCKF algorithm.

Multi-innovation adaptive Kalman filter algorithm for estimating the SOC of lithium-ion batteries based on singular value decomposition and Schmidt orthogonal transformation

The state of charge (SOC) of lithium battery is a key parameter for effective management of battery management systems (BMS). To address the problems of low precision, complex computation and poor robustness of traditional charging state estimation methods, an enhanced algorithm based on Unscented Kalman filter (UKF) is proposed. The singular value decomposition (SVD) method is adopted to ensure the normal operation of the Unscented Kalman Filter (UKF) algorithm even when the matrix P lacks positive semi-definiteness from a mathematical perspective. This enhancement significantly improves the theoretical robustness of UKF. Schmidt orthogonal transformation is concurrently used to reduce the computational complexity in the sampling point selection process, and the multi-innovation theory is combined with adaptive noise control to further improve the accuracy of SOC estimation. The algorithm is validated using the Urban Dynamometer Driving Schedule (UDDS) condition. The simulation results are excited using Singular value decomposition-multi-innovation adaptive Schmidt orthogonal unscented Kalman filter method (SVD-MIASOUKF). 0.95 % and 1.29 % of maximum errors are obtained at 25 °C and −10 °C, while the maximum errors are 2.46 %–2.99 % using SVD-UKF and UKF. The proposed approach shows faster convergence speed and higher estimation accuracy in comparison to traditional algorithms.

Dynamic state awareness for distribution network based on robust adaptive cubature kalman filter

With the rapid development of the economy and society, the demand for power quality is constantly increasing. As a crucial part of grid situational awareness, distribution network state estimation plays a vital role in providing critical data support for other advanced applications, which is significant for ensuring the safe and reliable operation of the distribution network. Therefore, this paper proposes a dynamic state awareness method for distribution networks based on the robust adaptive cubature Kalman filter (RACKF). The proposed solution, grounded on the core computational concept of the cubature Kalman filter (CKF), constructs a robust noise statistical estimator (NSE) composed of a biased NSE and an unbiased NSE to adapt to the unknown and time-varying process noise parameters in the dynamic state estimation process. The proposed solution can ensure that the calculated process noise parameters always meet the constraints and guarantee the robustness of the algorithm. In addition, an estimation strategy for the fusion of multi-time scale measurement data is developed according to the RACKF-based dynamic state estimation features in order to realize system state corrections and updates. The results of simulation experiments and comparisons with traditional CKF methods demonstrate the accuracy and superiority of the proposed solution.

Adaptive Fault‐Tolerant Multiplicative Attitude Filtering for Small Satellites

ABSTRACTThis study tackles the problem of fault‐tolerant attitude estimation for small satellites. A probabilistic adaptive technique is presented for the multiplicative extended Kalman filter (MEKF) algorithm that is used in attitude estimation. The presented method is based on tracking the normalized measurement innovations in the filter and calculating the probability of the normal operation of the estimation system. Using this probability, the filter gain is corrected to maintain the tracking performance of the filter despite faulty measurements. In order to evaluate the performance of this method, several simulations are performed where different types of faults are introduced to the synthetic attitude sensor measurements (magnetometer and sun sensor) at different times. Simulation results are compared not only with a conventional EKF but also with another popular adaptive Kalman filter, an adaptive Kalman filter with multiple scaling factors (MSFs).

Inspection robot GPS outages localization based on error Kalman filter and deep learning

In urban environments, inspection robots face complex terrain and variable motion states, posing high demands on their positioning systems. Although the integration of Micro-Electro-Mechanical Systems Inertial Navigation Systems (MEMS-INS) with the Global Positioning System (GPS) provides continuous positioning information, high buildings and tunnels in cities can block GPS signals, leading to signal interruptions and increased positioning errors. During GPS outages, MEMS-INS gradually accumulates errors, severely affecting positioning accuracy. To address this issue, this paper proposes an adaptive error state Kalman Filter (AESKF), which employs an adaptive mechanism to eliminate the noise impact of MEMS-INS and reduce reliance on the process model. Additionally, a deep learning framework based on the Self-Attention mechanism of the Transformer and a custom loss function Long Short-Term Memory (LSTM) module is proposed to predict position increments of the inspection robot. Combining AESKF with Transformer-LSTM achieves optimized positioning accuracy of the inspection robot during GPS outages in dynamic urban environments. Simulation and practical experimental results demonstrate that the combination of AESKF and Transformer-LSTM significantly improves positioning accuracy. Compared to other mature methods, the Root Mean Square Error (RMSE) of positioning is reduced by up to 83.64 % in the north direction and 89.56 % in the east direction. When the GPS signal interruption lasts for 10 s and 60 s, the maximum position error standard deviation (STD) is 0.1186 m and 1.0417 m, respectively.

Fuzzy Adaptive State Estimation of Distributed Drive Electric Vehicles with Random Missing Measurements and Unknown Process Noise

Accurate estimation of sideslip angle and vehicle velocity is crucial for effective control of distributed drive electric vehicles. However, as these states are not directly measured, Kalman-based approaches utilizing in-vehicle sensors have been developed to estimate them. Unfortunately, existing methods tend to ignore the impact of data loss on estimation performance. Furthermore, the process noise, which changes dynamically due to varying driving conditions, is not adequately considered. In response to these constraints, we propose a novel method called the fuzzy adaptive fault-tolerant extended Kalman filter (FAFTEKF). Initially, a fault-tolerant EKF is devised to handle missing measurements. Additionally, a fuzzy logic system that dynamically updates the process noise matrix, is built to improve estimation accuracy under different driving conditions. Extensive experimental results validate the superiority of the FAFTEKF over the traditional EKF across various scenarios with different degrees of data loss.

Interacting multiple model adaptive robust Kalman filter for process and measurement modeling errors simultaneously

This paper proposes an effective Interactive Multiple Model Adaptive Robust Kalman Filter (IMMARKF) without time delay to handle situations where both process modeling errors and measurement modeling errors exist simultaneously. Building upon the robust Centered Error Entropy Kalman Filter (CEEKF) for outlier measurements and the Adaptive Kalman Filter (AKF) for process modeling errors, the IMMARKF method combines the Gaussian optimality of the KF, the adaptability of AKF, and the robustness of CEEKF using the interacting multiple model (IMM) principle to adapt reasonably to changing application environments, and can obtain estimation results in the absence of time delay. Target tracking simulations show that compared to existing methods, the proposed method can better adapt to non-stationary noise and application environments where process anomalies and measurement anomalies occur simultaneously.

Vehicle posture wheelbase preview control of in-wheel motors drive intelligent vehicle on potholed road

The in-wheel motors drive intelligent vehicle (IMDIV) has a strong ability of dynamic control, which makes it be a major development path of intelligent vehicles in the future. However, its stability is easily deteriorated by the impact of the road when driving on potholed road. To tackle this issue, a vehicle posture control method based on road feedback and elevation recognition is proposed. Firstly, an elevation recognition algorithm of adaptive Kalman filter (AKF) based on vehicle dynamic response is proposed after considering the flooded road and the system noise uncertainty. Secondly, a vehicle posture controller of fuzzy active disturbance rejection control (FADRC) is designed, with the function of dynamically adjusting the active disturbance rejection control (ADRC) parameters. It is designed to implement front suspension feedback control and rear suspension wheelbase preview control. At last, the road elevation recognition algorithm and vehicle posture control method are proved by Simulink simulation and off-line hardware in the loop test. The results revealed that the AKF can effectively recognize both white noise pavement and potholed road, and the recognition accuracy is greater than 90%. The FADRC controller realizes accurate front suspension feedback control and rear suspension wheelbase preview control by adjusting the real-time online parameters of ADRC. The proposed vehicle posture control method can effectively control the pitch and roll motion, which significantly improves the stability of IMDIV on potholed road. This study can serve as a reference for the posture stability control of IMDIV on potholed road.

Innovation Adaptive UKF Train Location Method Based on Kinematic Constraints

To address the issue of reduced positioning accuracy caused by satellite signal interruptions when trains pass through long tunnels, a novel train positioning method based on an innovative adaptive unscented Kalman filter (UKF) under kinematic constraints is proposed. This method aims to improve the accuracy of the location of trains during operation. By considering the dynamic characteristics of the train, a dynamic kinematic-constrained inertial navigation system (INS)/odometer (ODO) combination positioning system is established. This system utilizes kinematic constraints to correct the accumulated errors of the INS. Additionally, the algorithm incorporates real-time estimation of the measurement noise covariance using innovation sequences. The updated adaptive estimation algorithm is applied within the UKF framework for nonlinear filtering, forming the innovative adaptive UKF algorithm. At each time step, the difference between the ODO sensor data and the INS output is used as the measurement input for the innovative adaptive UKF algorithm, enabling global estimation. This process ultimately yields the actual positioning result for the train. Simulation results demonstrate that the innovative adaptive UKF train positioning method, incorporating kinematic constraints, effectively mitigates the impact of satellite signal interruptions. Compared with the traditional INS/ODO positioning method, the innovative adaptive UKF method reduces position errors by 34.35% and speed errors by 36.33%. Overall, this method enhances navigation accuracy, minimizes train positioning errors, and meets the requirements of modern train positioning systems.

Robustness estimation for state-of-charge of a lithium-ion battery based on feature fusion

State of charge (SOC) of the lithium-ion battery stands as one of the crucial parameters of the battery management system. To enhance the robustness and accuracy of data-driven methods for estimating SOC, in this study, a novel framework based on feature selection and closed-loop estimation framework is proposed for estimating the SOC of a battery. Firstly, the maximum mutual information coefficient is used to correlate the data collected from the battery experiments. Secondly, an improved least squares support vector machine model (LSSVM) is proposed for SOC estimation using the sine cosine optimization algorithm for parameter optimization of LSSVM. Furthermore, based on the Sage-Husa adaptive Kalman filter, this study constructed a closed-loop estimation model. Finally, we conduct experiments on batteries with variable temperatures and working conditions, to verify its robustness and generalization. The results indicate that the proposed method has great SOC estimation accuracy compared to the control group. Even under simulated measurement noise conditions, the proposed method achieves the root mean square error 1.28 % and 1.12 % respectively, demonstrating strong robustness.

A robust adaptive error state Kalman filter for MEMS IMU attitude estimation under dynamic acceleration

Accurate estimation of attitude (pitch, roll) is a prerequisite for ensuring safe navigation during vehicle control execution. In dynamic environments, the presence of acceleration often degrades the accuracy and robustness of attitude estimation using traditional algorithms with Micro-Electro-Mechanical Systems (MEMS) Inertial Measurement Unit (IMU). This paper proposes a robust adaptive error state Kalman filter (RAESKF) algorithm for attitude estimation of MEMS IMU under dynamic acceleration conditions. The RAESKF algorithm decomposes the true attitude Direction Cosine Matrix (DCM) into nominal and error components. An error state Kalman filter is utilized to fuse real-time measurements from MEMS gyroscope and accelerometer, estimating the error component, which is then used to correct the nominal attitude DCM. Furthermore, within the error state Kalman filtering framework, a dynamic acceleration robust adaptive adjustment strategy is implemented. This strategy relies on real-time data monitoring, threshold-based decision-making, and switching mechanisms. It adaptively selects between dynamic acceleration model compensation and online adjustment of the measurement noise covariance matrix. The primary objective of this strategy is to mitigate the impact of disturbance induced by dynamic acceleration on attitude estimation, thereby enhancing the accuracy and robustness. Laboratory rotation experiments have demonstrated that the algorithm improved pitch and roll measurement accuracy by at least 8.81% and 11.69%, respectively, under rotational conditions. In dynamic acceleration conditions, pitch and roll measurement accuracy improved by at least 42.76% and 67.21%, respectively.

An Adaptive Strong Tracking Volume Kalman Filter Algorithm

Abstract Based on dental implant technology, this paper studies the position and posture tracking of surgical tools during the treatment of patients. A strong tracking adaptive volume Kalman filter (STF-ACKF) algorithm is proposed to meet the requirements of high accuracy, low time delay and strong robustness due to the complexity of the oral space and the narrow motion environment, to improve the measurement accuracy and reduce the noise interference. The adaptive module is added to the algorithm, and the real-time correction of process noise variance is realized by using MAP estimator [1-3]. The variance of the measured noise [4-5] was estimated using the variational Bayes (VB) method. Finally, the theoretical analysis and simulation results show that the mean error of STF-ACKF on X-axis, Y-axis and yaw angle is reduced by 1.17 mm, 0.76 mm and 0.62 ° respectively, the estimation accuracy and stability are improved significantly.

Adaptive approach to spectrum monitoring in cognitive radio networks through signal detection optimization

The article considers the improvement of the adaptive algorithm of the spectral monitoring method for cognitive radio networks by introducing adaptive wavelet transforms and filters. The use of adaptive Morle and Dobechy wavelet transforms, as well as adaptive Kalman, LMS, and RLS filters is proposed, which allows dynamically changing parameters depending on the conditions of the radio environment. The comparative analysis with traditional methods showed that adaptive methods significantly increase the efficiency of signal detection in conditions of low SNR values, reducing the noise level, improving the accuracy of signal detection and reducing the probability of false alarms. The results of the study confirm the perspective of using adaptive methods to increase the reliability and efficiency of spectral monitoring in real operating conditions.

Enhancing the state-of-charge estimation of lithium-ion batteries using a CNN-BiGRU and AUKF fusion model

Accurate estimation of lithium-ion batteries’ state of charge (SOC) is crucial for the safety of energy storage devices, preventing issues such as overcharging or discharging. This paper introduces a fusion model combining convolutional neural network (CNN), bidirectional gated recurrent unit (BiGRU), and adaptive unscented Kalman filter (AUKF). This method's advantage lies in integrating Kalman filtering with the benefits of neural networks, eliminating the need for complex hyperparameter tuning and battery model construction. Initially, CNN-BiGRU maps variables like voltage, current, and temperature to SOC for initial estimation. The AUKF algorithm then filters these SOC outputs, minimizing fluctuations and enhancing accuracy. This approach ultimately leads to precise and stable SOC estimates. To validate the model's effectiveness, lithium-ion battery datasets across various temperatures were extensively trained and tested. The CNN-BiGRU-AUKF model demonstrated consistent performance under these conditions, with a maximum MSE of 0.00011, MAE under 0.0092, Max AE around 0.02, and a maximum RMSE of 0.017. Compared to similar methods, the proposed approach demonstrates superior SOC estimation accuracy and computational efficiency. Additionally, the model's scalability was validated using training and testing data for SOC estimates from a different type of lithium battery.

A generic fusion framework integrating deep learning and Kalman filter for state of charge estimation of lithium-ion batteries: Analysis and comparison

Lithium-ion batteries (LIBs) are extensively utilized in power and energy storage systems. Accurately estimating state of charge (SOC) of LIBs using single methods is still challenging to fully address the problem associated with SOC. This paper proposes a novel generic fusion framework that integrates deep learning (DL) and Kalman filter (KF), characterized by an effective fusion of the results obtained by multiple-methods. Within the DL-based method, a spatial-temporal awareness model and an improved dung beetle optimizer are proposed to enhance the capture of spatial-temporal features and optimize hyperparameters. Additionally, three adaptive nonlinear KFs are employed for SOC estimation based on a simplified electrochemical model, with the adaptive cubature KF emerging as the most suitable following comparative analysis. Subsequently, the results from both approaches are integrated to derive the final result using various fusion methodologies. The effectiveness of the fusion framework is validated using experimental data, with kernel ridge regression emerging as the optimal fusion method. The best fusion results yield a mean absolute error of 0.2341% and a root mean square error of 0.3072%, demonstrating that proposed framework can effectively process and utilize multiple-source information, thereby enhancing accuracy and robustness compared to single methods and exhibiting adaptability to complex situations.

A Novel Estimating Algorithm of Critical Driving Parameters for Dual-Motor Electric Drive Tracked Vehicles Based on a Nonlinear Observer and an Adaptive Kalman Filter

High-speed dual-motor electric drive tracked vehicles (DDTVs) have emerged as a research hotspot in the field of tracked vehicles in recent years due to their advantages in fuel economy and the scalability of electrical equipment. The emergency braking of a DDTV at high speed can lead to slipping or even yawing (which is caused by a large deviation of forces at each track directly), posing significant challenges to the vehicle’s stability and safety. Therefore, the accurate real-time acquisition of critical driving parameters, such as the longitudinal force and vehicle speed, is crucial for the stability control of a DDTV. This paper developed a novel estimating algorithm of critical driving parameters for DDTVs equipped with conventional sensors such as rotary transformers at PMSMs and onboard accelerometers on the basis of their dynamics models. The algorithm includes a sensor signal preprocessing module, a longitudinal force estimation method based on a nonlinear observer, and a speed estimation method based on an adaptive Kalman filter. Through hardware-in-loop experiments based on a Speedgoat real-time target machine, the proposed algorithm is proven to estimate the longitudinal force of the track and vehicle speed accurately, whether the vehicle has stability control functions or not, providing a foundation for the further development of vehicle stability control algorithms.

HRTracker: Multi-Object Tracking in Satellite Video Enhanced by High-Resolution Feature Fusion and an Adaptive Data Association

Multi-object tracking in satellite videos (SV-MOT) is an important task with many applications, such as traffic monitoring and disaster response. However, the widely studied multi-object tracking (MOT) approaches for general images can rarely be directly introduced into remote sensing scenarios. The main reasons for this can be attributed to the following: (1) the existing MOT approaches would cause a significant rate of missed detection of the small targets in satellite videos; (2) it is difficult for the general MOT approaches to generate complete trajectories in complex satellite scenarios. To address these problems, a novel SV-MOT approach enhanced by high-resolution feature fusion and a two-step association method is proposed. In the high-resolution detection network, a high-resolution feature fusion module is designed to assist detection by maintaining small object features in forward propagation. By utilizing features of different resolutions, the performance of the detection of small targets in satellite videos is improved. Through high-quality detection and the use of an adaptive Kalman filter, the densely packed weak objects can be effectively tracked by associating almost every detection box instead of only the high-score ones. The comprehensive experimental results using the representative satellite video datasets (VISO) demonstrate that the proposed HRTracker with the state-of-the-art (SOTA) methods can achieve competitive performance in terms of the tracking accuracy and the frequency of ID conversion, obtaining a tracking accuracy score of 74.6% and an ID F1 score of 78.9%.

An online reconstruction method of dynamic loading based on adaptive tracking dual nested Kalman filter

Accurately reconstructing the unknown dynamic loading is crucial for controlling the vibration of mechanical systems. Many methods have been proposed for load identification of time-invariant systems, but in some mechanical systems, their structural parameters exhibit time-varying dynamic characteristics during their operation. Therefore, tracking the time-varying structural parameters to update the transfer function is necessary, which is the most important prerequisite for load reconstruction. However, some existing methods are unstable because of the nonlinear conditions. To overcome this issue, an improved dual-nested Kalman filter framework has been proposed. This method allocates unknown variables to two Kalman filters, allowing them to iterate and loop with each other. As a result, it achieves linear reconstruction of the dynamic loading for a time-varying system. The proposed method has been validated in two numerical examples: one is a spring-mass system with abruptly changing mass parameters, and the other is a milling system with slowly changing mass parameters. The results show that the proposed method can reconstruct loading stably and is not susceptible to noise interference.

UVIO: Adaptive Kalman Filtering UWB-Aided Visual-Inertial SLAM System for Complex Indoor Environments

Precise positioning in an indoor environment is a challenging task because it is difficult to receive a strong and reliable global positioning system (GPS) signal. For existing wireless indoor positioning methods, ultra-wideband (UWB) has become more popular because of its low energy consumption and high interference immunity. Nevertheless, factors such as indoor non-line-of-sight (NLOS) obstructions can still lead to large errors or fluctuations in the measurement data. In this paper, we propose a fusion method based on ultra-wideband (UWB), inertial measurement unit (IMU), and visual simultaneous localization and mapping (V-SLAM) to achieve high accuracy and robustness in tracking a mobile robot in a complex indoor environment. Specifically, we first focus on the identification and correction between line-of-sight (LOS) and non-line-of-sight (NLOS) UWB signals. The distance evaluated from UWB is first processed by an adaptive Kalman filter with IMU signals for pose estimation, where a new noise covariance matrix using the received signal strength indicator (RSSI) and estimation of precision (EOP) is proposed to reduce the effect due to NLOS. After that, the corrected UWB estimation is tightly integrated with IMU and visual SLAM through factor graph optimization (FGO) to further refine the pose estimation. The experimental results show that, compared with single or dual positioning systems, the proposed fusion method provides significant improvements in positioning accuracy in a complex indoor environment.